Dilate polygon EFGH with a scale factor of 2 and a center of dilation at point P. Start by plotting point F's corresponding point.
Start by looking at point F. To plot point F's corresponding point, first think about the distance between point F and the center of dilation. How many units is point F from the center of dilation, point P?
·	?	=	?
Point F's distance to the center of dilation	·	Scale factor	=	Corresponding point's distance to the center of dilation


To dilate point **F** with a scale factor of 2 from the center of dilation at point **P**, we need to follow these steps:

1. **Measure the distance between point F and point P**: 
   - Let’s say the distance between point F and point P is denoted as \( d(F, P) \).

2. **Calculate the new distance to the corresponding point**:
   - Multiply the distance between F and P by the scale factor. Since the scale factor is 2, the corresponding distance would be \( 2 \times d(F, P) \).

3. **Direction and positioning**:
   - The corresponding point \( F' \) will be in the same direction from point P as point F, but twice as far.

The general formula to find the new distance is:

\[
\text{Distance from } F' \text{ to } P = 2 \times d(F, P)
\]

Now, plot point \( F' \) at a distance that is twice as far from P in the same direction as the original point F.

### Next steps:
- Determine the coordinates of point P and point F.
- Calculate the distance between them.
- Multiply the distance by the scale factor.
- Plot the new point \( F' \) accordingly.

Do you have the coordinates for points P and F, or would you like to proceed with a general example?

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Here are five questions to further explore the concept:

1. What happens to the shape of a polygon when it's dilated with a scale factor greater than 1?
2. How would you dilate a polygon with a scale factor of less than 1?
3. What would change if the center of dilation were at the origin (0,0)?
4. How does the direction of dilation change if the center of dilation is outside the polygon?
5. Can a dilation ever make a shape smaller? Why?

**Tip**: When dilating, the angles of the polygon remain unchanged, but the distances between points increase or decrease by the scale factor.

Dilate polygon EFGH with a scale factor of 2 and a center of dilation at point P. Start by plotting point F's corresponding point. Start by looking at point F. To plot point F's corresponding point, first think about the distance between point F and the center of dilation. How many units is point F from the center of dilation, point P?

Learn how to dilate polygon EFGH with a scale factor of 2 and a center of dilation at point P. This geometry problem covers the key concepts of dilations and transformations, including calculating distances and applying scale factors. Suitable for students in Grades 8-10.

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